Comparing Two Hash Functions for Multi-Party Computation and Zero-Knowledge

Cryptographic hash functions are a paramount building block in cryptography and are used for numerous applications. The hash function Poseidon is widely favored for zero-knowledge applications (e.g. FileCoin, Dusk Network, LoopRing), and has been tailor designed for this purpose. The hash function Hydra is optimized to be computed in MPC. Hydra was presented in Eurocrypt 2023 and has less total number of rounds and transmitted data than its competitors. Zero knowledge and MPC applications that prove or compute hash functions share many similarities in terms of the optimization criteria of the function. For applications that require both proving a hash function in zero-knowledge and computing a hash function in MPC we ask the natural question:

How do the hash functions Poseidon and Hydra, which are optimized for zero-knowledge and MPC applications, respectively, perform for the other application?

 

To answer this question, we compare the performance between Hydra and Poseidon for zkSNARKs and MPCs.